After you have put in your phone number on your e-Boks, shortly after you will receive a text message to confirm, that you are the owner of the number. The text message is sent from 20 90 29 23.
You can confirm that the phone number is yours in various ways, e.g. by inserting the 4 digit code from the text message, into your e-Boks.
You can do so by going to Menu and then Profile, then click confirm phone number.
After you have confirmed the phone number, you can receive text messages about new documents, and NemSMS from the danish municipalities.